Question

show that 2-root 3 is irrational number​

Answer 1

Step-by-step explanation:

Let 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3=p/q

√3=p/q-2

√3=(p-2q)/q

p,q are integers then (p-2q)/q is a rational number.

But this contradicts the fact that √3 is an irrational number.

So,our supposition is false.

Therefore,2+√3 is an irrational number.

Hence proved.

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Answer 2

here's Ur answer

2-√3

we know that √3 is an irrational number

let us assume that 2-√3 is an rational number

so it can be written in the form of a/b , b≠0

so 2-√3=a/b

√3=2-a/b

here a, b and 2 are integers . so,2-a/b is rational

so √3 is also rational

but this contradicts the fact taht √3 is irrational (as we know it is irrational)

this contradiction has rise due to our wrong assumption of 2-√3 as rational.

hence, it is irrational

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